I wrote a minimal iOS app called PocketServer (~1MB in download size) that creates persistent local HTTP/WebDAV servers which can actually run in the background.
Features:
Serve a folder via WebDAV — browse/add/delete files from others devices on the same network.
Host a static website or directory listing, accessible locally.
Share files cross-platform on the same network, no app needed on the receiving side.
Why
There are already iOS apps for cross-platform file sharing, local HTTP servers, the reason I wrote PocketServer:
A lightweight app you can download even on slow connections (1MB is 2 minutes on 2G). Imagine not wanting to use the cloud, but still being asked to download a 50–100MB app just to share a file.
Background HTTP/WebDAV servers that keep running even when you switch apps.
Ramen for next month.